As a continuous‐wave signal builds up in an energized laser dye solution, the lifetimes for the excited state of the molecules become shorter than their orientational relaxation time. Physical consequences of the phenomomenon are considered for two extreme situations—transmission through pure mobile and pure rigid media continua, respectively. The dye is treated as a linear oscillator and spectral properties are assumed to be unchanged between the media. Two problems are examined, namely signal propagation and the extraction of energy at apointinthemediumfor a number of configurations of pump and signal polarizations, transverse or longitudinal excitations. Signal gradients and steady‐state conversion efficiencies are presented algebraically and graphically. A mobile medium has one of the steepest gradients, the largest energy storage, and one of the highest conversion efficiencies. Nevertheless, performance of a transversely excited, single‐pass amplifier for the commonly used configuration where pump and signal are plane polarized and have a shared polarization axis (ConfigurationC) shows little difference between rigid or mobile media, according to this analysis. For a rigid ConfigurationC, only about 21% of the dye molecules carry most of the signal load, in contrast with a mobile medium where all molecules work equally, and such a restricted distribution undergoes rapid turnover of its excited state. Twisting of the signal plane of polarization in a dye amplifier is confirmed.